THE JOURNAL OF CHEMICAL PHYSICS 130, 234304 !2009"
A laboratory and theoretical study of protonated carbon disulfide, HSCS+
M. C. McCarthy,1,a! P. Thaddeus,1 Jeremiah J. Wilke,2 and Henry F. Schaefer III2
1
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA
and School of Engineering and Applied Sciences, Harvard University, Cambridge,
Massachusetts 02138, USA
2
Center for Computational Quantum Chemistry, University of Georgia, 1004 Cedar St, Athens,
Georgia 30602, USA
!Received 3 March 2009; accepted 25 April 2009; published online 16 June 2009"
The rotational spectrum of protonated carbon disulfide, HSCS+, has been detected in the
centimeter-wave band in a molecular beam by Fourier transform microwave spectroscopy.
Rotational and centrifugal distortion constants have been determined from ten transitions in the
Ka = 0 ladder of the normal isotopic species, HS13CS+, and DSCS+. The present assignment agrees
well with high-level coupled cluster calculations of the HSCS+ structure, which, like earlier work,
predict this isomer to be the ground state on the HCS+2 potential energy surface; HCSS+, an isomer
with C2v symmetry, is predicted to lie more than 20 kcal/mol higher in energy. Other properties of
HSCS+ including its dipole moment, anharmonic vibrational frequencies, and infrared intensities
have also been computed at the coupled cluster level of theory with large basis sets. Because carbon
disulfide possesses a fairly large proton affinity, and because this nonpolar molecule may plausibly
exist in astronomical sources, HSCS+ is a good candidate for detection with radio telescopes in the
submillimeter band where the stronger b-type transitions of this protonated cation are predicted to
lie. © 2009 American Institute of Physics. #DOI: 10.1063/1.3137057$
I. INTRODUCTION
Carbon disulfide is isovalent to carbonyl sulfide and carbon dioxide, two molecules which have been used to understand how protonation affects electronic and molecular structure. Although the proton can bind to either of two isovalent
atoms at opposite ends of OCS,1 protonation to the terminal
atom of either CO2 or CS2 yields a single isomer. The rotational spectrum of HOCO+ !Refs. 2 and 3" has been known
for some time, and that of HOCS+ !Refs. 4 and 5" and
HSCO+ !Ref. 6" has now been measured. Somewhat surprisingly, there is no high-resolution data for HSCS+, even
though the proton affinity of CS2 #682 kJ/mol !Refs. 7–9"$ is
greater than that of both OCS #628 kJ/mol !Ref. 9"$ and CO2
#541 kJ/mol !Refs. 7 and 9"$. In addition, the rate coefficient
for the proton transfer reaction H+3 + CS2 → HCS+2 + H2 is
more than twice that with either OCS or CO2.10,11 Rotational
lines of the thioformyl ion HCS+ are readily observed in
electrical discharges with CS2.12,13
Detection of protonated carbon disulfide in the radio
band would be useful for several reasons. It would contribute
to our comparative understanding of the isovalent cations
HCO+2 , HOCS+, and HCS+2 , by providing a precise determination of its abundance relative to the parent molecule and
detailed information on its molecular structure and bonding.
HCS+2 may also serve as a convenient surrogate for nonpolar
CS2, which, like CO2 !or N2", cannot be observed directly by
microwave spectroscopy. HOCO+ has been detected toward
the Galactic Center clouds Sgr B2 and Sgr A,14–17 a few cold
starless clouds,18 and recently in the low-mass protostar
a"
Electronic mail: [email protected].
0021-9606/2009/130"23!/234304/6/$25.00
L1527.19 HOCS+ and HCS+2 may also be abundant in
space;20,21 if so, detection of HSCS+ would allow one to infer
the column density of CS2 and to better constrain the dissociative electron recombination rates of the ion.
There are not many spectroscopic and theoretical studies
of protonated carbon disulfide. The existence of this ion was
first established by mass spectrometry,7 a work which also
provided an experimental determination of the CS2 proton
affinity. The first ab initio study of HSCS+ was undertaken
by Taylor and co-worker,22,23 who computed the proton affinity and molecular geometry of this ion at the selfconsistent field level of theory. In 2007, Ramesh et al.24 detected HSCS+ using neutralization-reionization mass
spectrometry, and undertook density functional calculations
on the HSCS+ potential energy surface. In agreement with
the earlier work, the structure of ground state HSCS+ is similar to that of protonated OCS, with a nearly linear heavy
atom backbone, irrespective of the sulfur atom to which the
proton binds.
Motivated by the recent laboratory discovery of the elusive HSCO+ isomer,6 high-level coupled cluster calculations
have now been undertaken to better determine the structure
and properties of HSCS+, including vibrationally corrected
rotational constants and dipole moments, to assist spectroscopic identification of this ion. On the basis of these new
calculations, we here report the laboratory detection of
HSCS+ in a supersonic molecular beam by Fourier transform
microwave !FTM" spectroscopy. From detection of the lowest three rotational transitions in the Ka = 0 ladder, effective
rotational and centrifugal distortion constants have been derived. Our identification has been confirmed by detection of
130, 234304-1
© 2009 American Institute of Physics
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234304-2
J. Chem. Phys. 130, 234304 "2009!
McCarthy et al.
rotational lines of HS13CS+ and DSCS+ at very near the frequencies predicted by the molecular structure.
1.146 Å
119.3°
H+
O
0.998 Å
1.234 Å
C
173.6°
II. COMPUTATIONAL DETAILS
Computations were performed with MOLPRO package
2006.1.25 Structures were computed at the CCSD!T" level of
theory. The CCSD!T" method includes a perturbative estimate of connected triple excitations,26,27 and has been shown
to be very accurate for the computation of molecular
geometries.28 The particular challenge in computing HSCS+,
in contrast to isovalent HOCO+,2,29 is the large number of 1s,
2s, and 2p core electrons on the two sulfur atoms. In this
regard, we employed the cc-pwCVQZ basis set,30 which includes additional core basis functions designed to accurately
describe core-core and core-valence correlation effects.
Centrifugal distortion constants, vibration-rotation interaction constants, and fundamental vibrational frequencies
were computed from a quartic force field through second
order vibrational perturbation theory !VPT2".31–35 Centrifugal distortion constants were computed in the S-reduced
representation.36 Internal coordinate derivatives were computed by finite differences of energy points and subsequently
transformed to Cartesian derivatives using the INTDER2005
program of Allen.37,38 The VPT2 analysis was performed
with the ANHARM program of Yamaguchi and Schaefer.39
Due to the large computational cost associated with computing cubic and quartic force fields with at the all electron
CCSD!T"/cc-pwCVQZ level, the equilibrium rotational constants and harmonic frequencies are reported from the
CCSD!T"/cc-pwCVQZ structure while the vibration-rotation
interaction constants, centrifugal distortion constants, and
anharmonic vibrational constants are derived from a hybrid
approximation. A frozen core CCSD!T"/cc-pVQZ computation was performed at each point with core effects approximated at the CCSD/cc–pwCVTZ level, similar to techniques
previously employed in combustion thermochemistry.40,41
The final energies in the quartic force field are therefore
given as
Efinal = ECCSD!T"!fc"/cc-pVQZ + !Ecore ,
!1"
!Ecore = ECCSD!ae"/cc-pwCVTZ − ECCSD!fc"/cc-pwCVTZ ,
!2"
where fc denotes frozen core and ae denotes all electrons
correlated. The hybrid approximation matches the more rigorous CCSD!T"/cc-pwCVQZ harmonic frequencies within
2 cm−1 and rotational constants within 15 MHz. The hybrid
approximation error in zero-point shift for rotational constants should therefore be negligible compared to the intrinsic error in the CCSD!T"/cc-pwCVQZ method.
Since gradients and force constants were computed by
numerical differentiation, dipole moments !computed relative to the center of mass" and harmonic infrared intensities
were not available from the CCSD!T"/cc-pwCVQZ computation. Dipole moments and intensities were therefore computed at the less expensive CCSD!T"!fc"/cc-pVTZ level using the ACESII package.42,43 Because theoretical vibrational
transition frequencies and intensities are not pertinent to the
present experimental work, these calculations are summa-
H+
90.2°
1.126 Å
O
1.357 Å
1.664 Å
C
S
176.4°
H+
1.350 Å
93.3°
1.502 Å
C
S
1.644 Å
S
175.6°
FIG. 1. Theoretical geometries of protonated carbon dioxide !Ref. 45", carbonyl sulfide !Ref. 1", and carbon disulfide !this work" in their ground states.
The components of the dipole moment are calculated to be 2.0 D along the
a-axis and 2.8 D along the b-axis for HOCO+ !Ref. 46"; 1.52 D and 1.18 D
for HSCO+ !Ref. 1"; 0.19 D and 1.09 D for HSCS+ !this work; see Table I".
rized in the supplementary material, deposited in the Electronic Physics Auxiliary Publication Service !EPAPS" of the
American Institute of Physics.44
The CCSD!T"/cc-pwCVQZ geometry of the parent
HSCS+ is given in Fig. 1. The two C–S bond lengths are
quite different, 1.64 and 1.50 Å, in comparison to 1.55 Å for
unprotonated CS2. The C–S bond length for the protonated
sulfur is therefore lengthened considerably, indicating more
single bond character, while the C–S bond to the unprotonated sulfur is somewhat shortened. The S–C–S moiety remains nearly linear, but does bend significantly from its CS2
shape to 176°. Because of the near linearity of the S–C–S
angle and the low mass of hydrogen, HSCS+ is almost a
prolate, symmetric top. Two other HSCS isomers were located, in agreement with the results of Ramesh et al.24 At the
CCSD!T"/cc-pwCVQZ level, a cyclic, C2v isomer of connectivity HCSS was found 20.9 kcal mol−1 above the global
minimum. A Cs isomer of connectivity HCSS was also found
71.6 kcal mol−1 above the minimum. Given the large energy
differences between isomers, we here only report results for
the parent HSCS+.
Even at the much more modest CCSD/cc-pVTZ level,
the rotational constants for Be and Ce differ from the more
rigorous CCSD!T"/cc-pwCVQZ results by less than 50 MHz.
We can therefore regard the CCSD!T"/cc-pwCVQZ rotational constants as very near the basis set and correlation
limit. In contrast, the value for Ae is very sensitive to the
position of the hydrogen. The full CCSD!T"/cc-pwCVQZ result differs from the hybrid approximation !1" by over 900
MHz and from the CCSD/cc-pVTZ result by over 50 GHz.
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Protonated carbon disulfide, HSCS+
III. EXPERIMENTAL DETAILS
The rotational spectrum of HSCS+ was detected by
means of FTM spectroscopy of a supersonic molecular
beam, a technique which has been used with remarkable success to study unstable molecules. It has proved to be particularly effective for the detection of new carbon, silicon, and
sulfur molecules in various states of ionization, whose rotational spectra are greatly simplified at the very low rotational
temperature that is readily achieved in a supersonic molecular beam source. Most newly discovered molecules in our
laboratory47 are neutral radicals and carbenes, but molecular
ions, both positive and negative, have been studied as well,
including, as mentioned, HSCO+. Reactive molecules are
created in the throat of a small supersonic nozzle by applying
a low-current dc discharge to a short gas pulse created by a
fast mechanical valve. The gas in the present work is CS2,
heavily diluted in a hydrogen buffer.
Before undertaking a search for HSCS+, the production
of DCS+ was first optimized by replacing hydrogen with deuterium as the buffer gas. As in previous work !see, e.g., Ref.
5", the strongest lines of this ion were observed at discharge
potential of 1000 V with CS2 diluted in D2 to "0.1%. Other
experimental parameters were similar to those which optimize HSCO+: The total flow rate was about 20 cm3 min−1 at
standard temperature and pressure, with a stagnation pressure
behind the valve of 2.5 kTorr !3.3# 105 Pa", and the nozzle
pulsed at 6 Hz. Under these conditions, the 1 → 0 line of
DCS+ near 36 GHz was observed with high signal-to-noise
ratio after only a few minutes of integration.
The search for the rotational spectrum of HSCS+ was
based on the high-level calculations described in Sec. II. Because zero-point corrections are fairly small, the equilibrium
!Be" and vibrationally-corrected !B0" rotational constants differ by less than 0.1%. If HSCO+ is a guide, the predicted
transition frequencies in the Ka = 0 ladder should be accurate
to better than $1%, an uncertainty which amounts to a
search of at most $200 MHz near 18.7 GHz, the predicted
frequency of the 30,3 → 20,2 line.
On the basis of the theoretical predictions, a search near
18.7 GHz was undertaken. Owing to the small calculated
dipole moment of HSCS+ along the a-inertial axis, high microwave power !%1 W" was used to saturate the rotational
line of this weakly polar cation. Only one unidentified line
!see Fig. 2", lying within a few tens of megahertz of the
scaled predictions, was found. Subsequently, two additional
lines nearly harmonic in frequency were detected at higher
!40,4 → 30,3" and at lower frequencies !20,2 → 10,1".
Searches for the analogous transitions of HS13CS+ using
an isotopically enriched sample of 13CS2, and DSCS+, with
D2 instead of H2 as the buffer gas, were then undertaken.
Because the carbon atom is very close to the center of mass,
transitions of HS13CS+ are shifted only very slightly !less
than 1 MHz" with respect to those of normal HSCS+, but are
still observed because the 13CS2 sample is of high purity
!%99%". For DSCS+, the theoretical rotational constants !see
Sec. II" were scaled by the ratio of the measured rotational
constant !Beff" to that calculated for the normal isotopic species !see Fig. 1". Such scaling generally yields isotopic fre-
J. Chem. Phys. 130, 234304 "2009!
Relative Intensity
234304-3
18704.6
18705.0
18705.4
Frequency (MHz)
FIG. 2. A portion of the rotational spectrum observed through an electrical
discharge of dilute CS2 in hydrogen showing the 3 → 2 transition of HSCS+,
the result of six min of integration. Each rotational transition has a doublepeaked line shape, the result of the Doppler shift of the Mach 2 molecular
beam relative to the two traveling waves that compose the confocal mode of
the Fabry–Pérot.
quency shifts !about 400 MHz for DSCS+" to better than
$1%, so a search of only a few megahertz in the vicinity of
18.3 GHz was required for detection.
IV. RESULTS
HSCS+ is a closed-shell, asymmetric top molecule near
the prolate limit !& = −0.9994". The Ka = $ 1 rotational ladders lie about 13 K above ground, but in our rotationally cold
molecular beam !Trot % 3 K", these are not well populated,
and, as a result, the rotational spectrum of HSCS+ consists of
single series of lines from Ka = 0. Those measured for HSCS+
and its two rare isotopic species are summarized in Table II.
Transitions in this ladder are well described by a simple
polynomial expansion in J!J + 1", where only the first two
terms !Beff and Deff" are needed to reproduce !see Table III"
the observed frequencies. Attempts to detect lines from Ka
= $ 1 ladders of both HSCS+ and DSCS+ were unsuccessful.
The spectroscopic and chemical evidence for the present
identification is extremely strong. The effective rotational
constant is within 0.1% of the ab initio value reported by
Taylor and Scarlett,22 and similarly good agreement is also
achieved with the coupled cluster results !Table III". Furthermore, the effective centrifugal distortion constant Deff, which
is dominated by contributions from two terms !Ref. 48, see
also Appendix C of Ref. 49", one from DJ #%0.36 kHz; see
Sec. II or that measured for ground state S13CS !Ref. 50"$,
the other from the asymmetry of a nearly prolate top molecule #b p = −6 # 10−5, where b p = !C − B" / !2A − B − C"; Ref.
51$, is close to that calculated for HSCS+. The absence of
lines at subharmonic frequencies indicates that the observed
lines are not from a larger or heavier molecule. The observed
lines also pass several other tests: They are only found in the
presence of an electrical discharge through a gas containing
H2 and CS2, as expected, and the lines of the normal isotopic
species disappear when H2 is replaced by D2 as the buffer
gas, indicating a hydrogen-containing molecule. Like either
DCS+ or HSCO+, all of the lines assigned to HSCS+ or its
isotopic species either are significantly broadened or disappear when a permanent magnet, which produces a small
!%2 G" field at the center of the Fabry–Pérot cavity, is
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234304-4
J. Chem. Phys. 130, 234304 "2009!
McCarthy et al.
TABLE II. Measured rotational transitions of isotopic HSCS+ !in MHz".
TABLE I. Rotational constants and dipole moments for HSCS+.
Rotational constants
Axisa
A
B
C
Equilibrium values
Zero-point values
Dipole
Moment
284 415
3139
3105
282 787
3133
3097
0.19
1.09
0.00
a
Rotational constants are given in MHz, and dipole moment !'" components
along the principal axes are given in Debye. Dipole origin is chosen as the
center of mass.
brought near the molecular beam. The origin for this effect is
that a static magnetic field produces a Lorentz force on fastmoving charged particles, which in turn increases the collisional cross section and therefore linewidth for light ions
such as protonated carbonyl sulfide5 and the butadiyne anion,
C4H−.52 The small permanent magnet field has no apparent
effect either on the discharge chemistry or on the linewidth
of closed-shell, neutral molecules.
Conclusive confirmation of HSCS+ is finally provided by
isotopic substitution: lines of the 13C and deuterium isotopic
species were observed within 0.3% of those calculated from
the molecular structure. The more than twofold increase in
the magnitude of Deff upon deuteration !Table III" is expected; it is a consequence of the fourfold greater asymmetry
of DSCS+!b p = −2 # 10−4" over HSCS+.
V. DISCUSSION
Detection of rotational lines of HSCS+ in the same
H2 / CS2 discharge where HCS+ is abundant is reassuring.
Because the lowest rotational transition of HCS+!42.6 GHz"
lies just above the frequency range of our FTM spectrometer,
it is not possible to directly compare relative intensities and
abundances for HCS+ and HSCS+, but such a comparison is
possible for DCS+ and DSCS+. Not surprisingly, the DCS+
line at 36 GHz is about ten times more intense than the
strongest line of DSCS+ at 18.3 GHz, owing to the large
difference in dipole moments #'a = 1.8 D for HCS+ !Ref. 53"
versus 0.19 D for HSCS+$. Taking this difference, the rotational partition function, and the instrument response of the
cavity at the two frequencies into account, however, we estimate that DSCS+ is only about four times less abundant
than DCS+, assuming the same rotational temperature !3 K"
for both cations. The greater abundance of DCS+ may arise
in part because of the higher proton affinity of CS #732 kJ/
mol !Ref. 54"$ relative to CS2. Like other protonated molecules recently observed with our spectrometer,5,6 we estimate #DSCS+$ / #CS2$ % 10−3, owing to the large difference in
the rates of proton transfer from H+3 versus electron recombination.
Although the a-type rotational spectrum of HSCS+ is
simple and readily identifiable, consisting of lines harmonically related by integer quantum numbers, the small a-dipole
moment of this cation !see Table I" may be the reason it has
not been observed previously in the radio band. Because line
intensities in absorption spectroscopy are proportional to the
square of the dipole moment, not the first power, as here with
the FTM spectrometer, lines of HSCS+ will be 100 times
JK! !,K! → JKa,Kca
HSCS+
HS13CS+
DSCS+
20,2 → 10,1
30,3 → 20,2
40,4 → 30,3
50,5 → 30,3
12 469.970
18 704.922
24 939.836
31 174.702
12 469.824
18 704.708
24 939.556
¯
12 188.815
18 283.150
24 377.390
¯
a
c
a
Note: estimated measurement uncertainties are 5 kHz.
weaker than those of HCS+ if both cations are present at the
same level of abundance. Although lines of HCS+ are quite
strong in a CS2 / H2 discharge,13,55 those of HSCS+ would be
marginally detectable at best if this decrement applies.
Additional spectroscopic studies at millimeter wavelengths are required to better determine the rotational spectrum and centrifugal distortion of HSCS+, and to undertake a
radioastronomical search for this cation. Higher-J transitions
in the Ka = 0 ladder can be extrapolated with precision from
the present data set, so a search of at most 10 MHz will
initially be required at 300 GHz, but these lines will undoubtedly be very weak in long path dc glow absorption
spectroscopy. More promising, but more challenging owing
to the large uncertainty in the A rotational constant, will be
detection of the b-type transitions of HSCS+ because of the
larger calculated dipole moment along this axis !1.1 D; see
Table I". Once found, it may then be feasible to detect transitions in higher ladders !Ka " 3" because these are low in
energy compared to the temperature of our dc glow discharge
!%200 K". With precise rest frequencies in hand, an astronomical search for the stronger b-type transitions of this protonated cation can then be undertaken.
There is a simple geometric explanation for the small
a-dipole moment of HSCS+ compared to those of either
HOCO+, HOCS+, or HSCO+. As shown in Fig. 1, proton
attachment to the one of the lone pairs on the terminal O
atom of nonpolar CO2 or OCS results in HCO bond angles of
120° or 180°, and thus substantial dipole moments along the
a-axis for these two cations. Protonation to the sulfur atom of
OCS results in a %90° HCS bond angle, but because OCS is
polar !' = 0.715 D; Ref. 56", the a-dipole moment of
HSCO+ !1.57 D; Ref. 1" is still significant. Because CS2 is
both nonpolar and fairly heavy, addition of a proton perpendicular to the heavy atom backbone does little to shift the
center of mass along the a-inertial axis; as a consequence,
HSCS+ has a small dipole moment along that axis !but a
much larger one along the b axis".
Other protonated molecules similar in structure and
composition to HSCS+ may be detectable with present techniques. Two obvious candidates would appear to be HOSO+
and HSO+. As pointed out by Millar et al.,57 the high fractional abundance of SO !%10−7 – 10−8; Ref. 58" and SO2
!%10−7 – 10−8; Ref. 59 and 60" in interstellar clouds implies
that both protonated species may be abundant there. Although the proton affinity of SO does not appear to have
been measured or calculated, that of SO2 !672 kJ/mol; Ref.
9" is substantial. In addition, recent theoretical calculations at
the CCSD!T"/cc-pwCVQZ level of theory by Thorwirth61
predicted that cis-HOSO+ and trans-HOSO+ are comparable
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234304-5
Protonated carbon disulfide, HSCS+
J. Chem. Phys. 130, 234304 "2009!
TABLE III. Spectroscopic constants of isotopic HSCS+ in the Ka = 0 ladder !in MHz".
HSCS+
HS13CS+
DSCS+
Constanta
This work
Theoretical
This work
Predicted
This work
Predicted
Beff
Deff # 103
3117.4965!13"
0.53!2"
3115b
0.48c
3117.4599!13"
0.48!5"
3117.4b
0.48c
3047.2141!13"
1.26!5"
3047.4b
1.20c
a
Note: Estimated uncertainties !in parentheses" are 1( in units of the last significant digit.
Derived from the HSCS+ structure shown in Fig. 1, in which the equilibrium rotational constants, calculated at
the CCSD!T"/cc-pwCVQZ level of theory, are corrected by zero-point vibrational effects !see Table I". For the
rare isotopic species, the predicted rotational constants have been scaled by the ratios of the measured constants
to those calculated for the normal isotopic species.
c
For the Ka = 0 ladder, Deff = DJ + !B − C"2 / #32!A − !B + C" / 2"$ has been derived from the theoretical rotational
constants of HSCS+ or those scaled for the rare isotopic species, assuming DJ = 0.36 kHz.
b
in stability, and that both possesses singlet ground states with
large dipole moments !1.7–3.2 D" along the a-inertial axis.
Both isomers also have at least two rotational transitions in
the Ka = 0 ladder which should be accessible with our FTM
spectrometer. Like HCS+, the fundamental rotational transition of HSO+!42.8 GHz" lies just above the frequency ceiling of our microwave spectrometer !42 GHz", but the same
transition of DSO+!40.2 GHz" should be accessible; the
large calculated a-dipole moment of this ion !2.9 D; Ref. 61"
should aid detection.
ACKNOWLEDGMENTS
We thank S. Thorwirth and C. A. Gottlieb for helpful
discussions. The work in Cambridge was supported by the
NSF under Grant No. CHE-0701204 and the NASA under
Grant No. NNX08AE05G; that in Georgia was supported by
the NSF under Grant No. CHE-0749868.
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